statistical relation between seismic velocity and resistivity

Statistical Estimation of Soil Type UsingCross-plots of S-wave Velocity and

Resistivity in Japanese Levees

*Koichi Hayashi, Geometrics

Tomio Inazaki, PWRI Tsukuba Central Institute

Kaoru Kitao, CubeWorks

Takaho Kita, TK Ocean-Land Investigations

Statistical Estimation of Soil Type Using Cross-plots of S-wave

Velocity and Resistivity in Japanese Levees 1

Outline of Integrated Geophysical Method forLevee Safety Assessment



• The method consists of a surface-wave method and

resistivity methods, such as a capacitively-coupled

resistivity method or an electro-magnetic method.

• The surface-wave method provides S-wave velocity

structure of levee body and fundation.

• The capacitively-coupled resistivity method or the

electro-magnetic method provides resistivity structure

of levee body and foundation.

• A cross-plot analysis of S-wave velocity and resistivity

estimates soil type of levee body and foundation.

Surface-wa e Method Using Land Streamer

"' Short.wavd ngth surfa<: wav s

)

3

Resistivity Method Using Capacitively

Coupled Resistivity (CCR)


In CCR, capacitors are used as

electrode and metallic stakes are

not used. The OhmMapper was

used as a CCR instrument


S-wave Velocity and N-value

(blow-count) obtained by SPT

0.1

10

Clay

Sand

Gravel

Others

1

100

0 50 100 150 200 250

S-wave velocity (m/sec)

300 350 400

N-

valu

e

N= 1.7 ∗ 10−4 ∗ 𝑉�2.1



20% Grain Size (D20) and Resistivity

0.001

0.01

0.1

1

10

10 100 1000

Resistivity (ohm- m)

10000

D2

0

(mm

)

Clay

Sand

Gravel



7

S-wave velocity and Resistivity forLevee Safety

• From theArchie’s equation, resistivity of soil mainly indicates soil type.

• S-wave velocity is mainly affected by shear strength or porosity.

• Safety of levees can be evaluated by S-wave velocity andresistivity.

S-wave velocity

Resistivity

High

Low

Low High

Soil type

Sandy

Clayey

S-wave velocity

Low

Low High

Resistivity

High

Danger (loose, sandy)

Safety

Safe (tight, clayey )

Shear strength(degree of compaction)

High(tight)Low(loose)

S-wave velocity and Resistivity forLevee Safety

8Velocity and Resistivity in Japanese Levees

• A soil type (clay, sand or gravel) or grain size distribution (clay

contents or D20) is the most important information for levee safety

evaluation from an engineering point of view.

• The soil type or the grain size distribution is used in many engineering

analyses

• In most of such analyses, the soil type or the grain size distribution is

obtained by the borings or laboratory tests.

• Physical properties obtained through the geophysical methods (e.g. S-

wave velocity or resistivity) do not directly relate to the soil type and

the grain size distribution.

• We are going to estimate the soil type in terms of a statistical

approach using geophysical and geotechnical data collected in Japan.



Statistical Estimation of Soil Type

• Soil type of levee body and foundation is statistically

estimated using cross-plots of S-wave velocity and

resistivity in Japan

• S-wave velocity and resistivity are collected from

• surface wave methods and resistivity methods.

• Total survey line length of the geophysical methods is

about 600km on 37 rivers in Japan.

• The blow counts and soil types are collected from about

• 400 boring logs carried out on geophysical survey lines.

• The total number of extracted data is about 4000.Statistical Estimation of Soil Type Using Cross-plots of S-wave

Example of Geophysical Sections

-6

-4

-2

-0

2

4

6

8

10

12

14

16

Depth

(m)

-100

12

14

16

018

2

4

6

8

100 183.4 0 500 700 900 1100 1300 1500 1700 1900 2100 2300 2500 2700 2900 3100

Distance (m)

S-wave velocity section

500

360

280

220

160

130

100

70

40

(m/s)

S-wave velocity

1020304050

9.9 S1-0G

1.1BS

GS

6.6S

8.0GS

10.6

GS

-6

-4

-2

-0

2

4

6

8

10

12

14

16

Depth

(m)

-100 100 183.4 0 500

12

14

16

018 700 900 1100 1300 1500 1700 1900 2100 2300 2500 2700

Distance (m)

2900 3100

Resistivity section

3000

1000

500

360

240

150

80

40

10

Ohm-m

Resistivity

1020304050

2

4

6

8

9.9 S1-0G

1.1BS

GS

6.6S

8.0GS

10.6

GS

S-wave velocity

Resistivity

Levee body (unsaturated)

Foundation (saturated)

Levee body (unsaturated)

Foundation (saturated)



Extracting Vs, Resistivity and Soil type

6

8

10

12

14

16

-6

Depth

(m)

-100 100 183.4 0 500

12

14

16

018 700 900 1100 13700.3 1500 17006 1900

8.3Distance (m2)3

9.3 20

10.3 24

12.3 29

13.3 33

14.3 31

15.3 35

16.3 19

2100 23202002500 2700 2190304 3100

S-wave velocity section

(m/s)

40

10070

130

220160

280

5003602

4

6

8

9.9 S1-0G

6.6S

8.0GS

10.6

GS

-6

-4

-2

-0

2

4

6

8

10

12

14

16

Depth

(m)

-100 100 183.4 0 500

12

14

16

018 700 900 1100 1300 1500 1700 1900 2100 2300 2500 2700 2900 3100

Distance (m)

Resistivity section

10

Ohm-m

sistivity

40

15080

240

500360

3000

1000

1020304050

2

4

6

8

9.9 S1-0G

1.1BS

GS

6.6S

8.0GS

10.6

GS

Levee body3.3 8 220 339 Gravel

4.4 10 259 378 Gravel

5.5 8 223 262 Gravel

6.3 8 223 262 Gravel

Foundation

Sand

243 134 Gravel

247 134 Gravel

247 93 Sand

Gravel

311 80 Gravel

311 80 Gravel

307 80 Gravel

307 73 Gravel

307 73 Gravel

17.3 39 307 73 Gravel



Depth N-value S-wave velocity Resistivity Soil type-4

-2(m) (m/sec) (ohm-m)

S-

wave velocity

-0

2

1.1BS

1020304050

1.3 42 230 226 Gravel

4 GS

2.3 9 230 256 Gravel

Re

11.3 20 297 93

Cross-plot of Vs and Resistivity

100

Re

sist

ivit

y(m

/se

c)

1

10

100

1000

10000

0


10000

1

10

100

1000

0 100

Levee body200 300 400 500

Foundation200 300 400 500

Re

sist

ivit

y(m

/se

c)




Sand

Gravel

Sand

Gravel

S-wave velocity Resistivit

y

Soil type

(m/sec) (ohm-m)

230

230

226

256

Grave

l

Grave

l

220 339 Gravel Levee

body

259 378 Gravel

223 262 Gravel

223

220

243247

262

134

134134

Grave

l

Sand

Grave

lGravel

247 93 Sand

297 93 GravelFoundation

311 80 Gravel

311 80 Gravel

307 80 Gravel

Resistivity and S-wave velocityfrom 400 Boring Logs

13

1

10

100

1000

10000

0 50 100 150 200 250 300 350 4

Vs (m/sec)

lay

and

ravel

thers

00 450 500

Re

sist

ivit

y(o

hm

-m

)

C

S

G

O

1

10

100

1000

10000

0 50 100 150 200 250 300 350 400 450 500

Vs (m /sec)

Res

isti

vity

(oh

m-

m)

Clay

Sand

Gravel

Others

Foundation

(saturated)

Levee body

(unsaturated)

1

10

100

1000

10000

Clay

0 450 500

Re

sist

ivit

y(o

hm

-m

)

Vs (m/sec)

1

10

100

1000

10000

Sand

450 500

Re

sist

ivit

y(o

hm

-m

)

Vs (m/sec)

1

10

100

1000

10000

Re

sist

ivit

y(o

hm

-m

)

Vs (m/sec)

Gravel

1

10

100

1000

10000

0 50 100 150 200 250 300 350 400

Vs (m/sec)

450 500

Re

sist

ivit

y(o

hm

-m

)

1

10

100

1000

0 50 100 150 200 250 300

Vs (m/sec)

350 400 450 500

Re

sist

ivit

y(o

hm

-m)

Sand

1

10

100

1000

0 50 100 150 200 250 300

Vs (m/sec)

350 400 450 500

Re

sist

ivit

y(o

hm

-m

)

ClaFy10000

S-wave velocity and Resistivity

10000

Gravel



oundation

Levee body

Clay Sand Gravel

Polynomial Approximation of Soil Type• Polynomial approximation (curved plane) is used to

estimate the soil type from the correlation between S-wave

velocity and resistivity.

• In the approximation, the soil type is represented by

discontinuous numbers one (clay), two (sand) and three

(gravel).

• Polynomial equation is a function of S-wave velocity (Vs)

and resistivity () and yields a continuous value S between

one and three.

• Coefficients of equation are optimized by least squares

method.

S avs bvs clog10 d log10evs log10 fvs log10 gvs log10h2 22 2



Soil Type and Represented Numbers



Soil type Represented

number

Number of data

Levee

body

Foundation

Clay 1.0 221 915

Sand 2.0 199 2145

Gravel 3.0 143 425

Total - 563 3485


10000

1000

Resis

ivity

(ohm

-m)

400 450 500

:Gravel (3.0)100



10

10 50 100 150 200 250 300 350

S-wave velocity (m/s)

:Clay

:Sand

Levee body

(1.0)(2.0)

Resis

tivity

(ohm

-m)

Sand (2.0)

Clay (1.0)10 50 100 150 200 250 300 350 400 450 500




:Clay (1.0):Sand (2.0):Gravel(3.0)

Gravel (3.0)

10000

1000

100

10

Polynomial ApproximationLevee body


10000

1000

100

10

Resis

tivity

(ohm

-m)

:Clay (1.0):Sand (2.0):Gravel (3.0)

10 50 100 150 200 250 300 350 400 450 500




Foundation

Sand (2.0)

Clay (1.0)10 50 100 150 200 250 300 350 400 450 500




:Clay (1.0):Sand (2.0)

:Gravel (3.0)

Gravel (3.0)

10000

1000

100

10

Resis

tivity

(ohm

-m)

Polynomial ApproximationFoundation

Polynomial Approximation

Clay

Sand

Gravel

10000

1000

100

10

1

R

e

is

tsvi

tiy(ohm

m-

)

400 450 5000 50 100 150 200 250 300 350

S-wavevelocity(m/s)

400 450 500

:Clay

:Sand

:Gravel

Clay

Sand

Gravel

10000

1000

100

10

1

Resis

tivity (

ohm

-m)

0 50 100 150 200 250 300 350

S-wavevelocity(m/s)

:Clay

:Sand

:Gravel

Clay



Sand

Gravel

Gravel

Sand

Clay

Foundation

(saturated)

Levee body

(unsaturated)

Polynomial Approximation of Soil Type

S avs bvs clog10 d log10evs log10 fvs log10 gvs log10h2 22 2



Levee body Foundationa -0.0000062

b -0.0072263

c 0.5333744

d -1.5275230

e 0.0000016

f -0.0025515

g 0.0111545

h 1.7115340

a -0.0000002

b 0.0019388

c 0.0938875

d -0.5366671

e -0.0000064

f 0.0001980

g 0.0032458

h 1.4068120

Example of EstimationS-wave velocity

Elevation (m) S-wave velocity

Levee body

Foundation

Distance (m)



Distance (m)

(m/sec)

ResistivityElevation (m) Resistivity

(Ohm-m)

Levee body

Foundation

Example of Estimation10000

1000

100

10

Resis

tivity

(ohm

-m)

10

1 0

Resis

tivity

(ohm

-m)

10000

1000

100

Levee body Foundation

Elevation (m)

Gravel (3.0)Levee body

Foundation

Soil type

Sand (2.0)

Clay (1.0)

Distance (m)



50 100 150 200 250 300 350 400 450 500 1 0 50 100 150 200 250 300 350 400 450 500

S-wave velocity (m/s) S-wave velocity (m/s)

Accuracy of Estimation



• Accuracy of estimation can be statistically

evaluated by comparing the estimated soil

parameter with actual soil.

• Data were grouped into four groups (1.0 to 1.5, 1.5

to 2.0, 2.0 to 2.5, 3.0 to 3.5) by the estimated soil

parameter.

• In each group, the numbers of actual soil type (clay,

sand, gravel) were counted as probability.

0% 20% 80% 100%

Soil type

Clay(1.0)

Sand(2.0)

Gravel(3.0)2.0 to 2.5

2.5 to 3.0

Proportion Fo

Esti

mat

edso

ilp

aram

ete

r

Levee body

Accuracy of Estimation


1.5 to 2.0

2.0 to 2.5

2.5 to 3.0

Proportion

Esti

mat

edso

ilp

aram

ete

r

Probability40% 60%

1.0 to 1.5

1.5 to 2.0

Levee body Foundation

0% 20% 80% 100%

1.0 to 1.5

undation

Soil type

Clay(1.0)

Sand(2.0)

Gravel(3.0)

Probability

40% 60%



Conclusions• The soil type of levee body and foundation was

statistically predicted using the cross-plots of S-wave velocity and of resistivity.

• The results imply that the physical properties obtained by geophysical methods, such as S-wave velocity andresistivity, can be used not only for qualitativeinterpretation but also quantitative engineering analyses,such as slope stability or liquefaction analyses.

• Similar approaches can be applied to other purposesbesides levee inspection and other countries besidesJapan.

• It is important that any results of geophysicalinvestigations are saved as a standard format and registered in database with adequate geotechnical or geological information.


statistical relation between seismic velocity and resistivity

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